If the median of the distribution given below is 28.5, find the values of x and y.

Class interval	Frequency
0 - 10	5
10 - 20	x
20 - 30	20
30 - 40	15
40 - 50	y
50 - 60	5
Total	60

Cumulative frequency distribution table is as follows :

We know that,

⇒ n = 60

⇒ 45 + x + y = 60

⇒ x + y = 15 ………..(1)

Given,

Median = 28.5

From cumulative frequency distribution table we get :

Median lies in class 20 - 30.

∴ Median class = 20 - 30

⇒ Lower limit of median class (l) = 20

⇒ Class size (h) = 10

⇒ Frequency of median class (f) = 20

⇒ Cumulative frequency of class preceding median class (cf) = 5 + x

By formula,

Median = $l + \Big(\dfrac{\dfrac{n}{2} - cf}{f}\Big) \times h$

Substituting values we get :

$\Rightarrow 28.5 = 20 + \Big(\dfrac{\dfrac{60}{2} - (5 + x)}{20}\Big) \times 10 \\[1em] \Rightarrow 28.5 - 20 = \dfrac{30 - 5 - x}{2} \\[1em] \Rightarrow 8.5 \times 2 = 25 - x \\[1em] \Rightarrow 17 = 25 - x \\[1em] \Rightarrow x = 25 - 17 = 8.$

Substituting value of x in equation (1), we get :

⇒ 8 + y = 15

⇒ y = 15 - 8

⇒ y = 7.

Hence, x = 8 and y = 7.